code: def forward(self, x: Tensor, adj_t: SparseTensor, *args) -> Tensor:
      if len(args) > 0:
          batch_size = args[0]
          n_id = args[1]
          P_bar = adj_t[:, batch_size:]
          P_tilde = P_bar.t()
      else:
          print("no batch_size in the forward of conv")
  
      if self.drop_input:
          x = F.dropout(x, p=self.dropout, training=self.training)
  
      for conv, bn, hist in zip(
          self.convs[:-1], self.bns, self.histories
      ):
          h = conv(x, adj_t)
          if self.batch_norm:
              h = bn(h)
          if self.residual and h.size(-1) == x.size(-1):
              h += x[: h.size(0)]
          h = h.relu_()
  
          if n_id is not None and batch_size is not None:
              with torch.no_grad():
                  if self.batch_norm:
                      bn.eval()
                      to_outbatch_emb = conv.propagation(
                          x[:batch_size].detach(), P_tilde
                      )
                      outbatch_emb = conv.transformation(
                          x[batch_size:].detach(), emb=to_outbatch_emb
                      )
                      outbatch_emb = bn(outbatch_emb).relu()
                      hist.forward(outbatch_emb, n_id[batch_size:])
                      bn.train()
                  else:
                      to_outbatch_emb = conv.propagation(
                          x[:batch_size].detach(), P_tilde
                      )
                      outbatch_emb = conv.transformation(
                          x[batch_size:].detach(), emb=to_outbatch_emb
                      ).relu()
                      hist.forward(outbatch_emb, n_id[batch_size:])
  
          x = self.push_and_pull(hist, h, *args)
          x = F.dropout(x, p=self.dropout, training=self.training)
  
      x = self.convs[-1](x, adj_t)
      return x
  
imports: from itertools import product
  from typing import Optional, List
  import tqdm
  import torch
  from torch import Tensor
  import torch.nn.functional
  from torch.nn import ModuleList, Linear, BatchNorm1d
  from torch_sparse import SparseTensor
  from torch_geometric.nn import MessagePassing
  from torch_geometric.nn import PNAConv
  from torch_scatter import segment_csr
  from ..models import ScalableGNN
label_desc: Use image node_id 5 for calling the PNA obj's underlying member method code with example usage: obj.forward(x, adj_t) and returns: x